Three Phenomena in DFT-based Spectrum Analysis

Three phenomena occur during spectrum analysis using DFT:

1. Aliasing: When sampling continuous signals, the signal must be band-limited with sufficiently high sampling frequency. Anti-aliasing filters should be implemented before sampling (e.g., using MATLAB's low-pass filter design functions like butter or cheby1) to satisfy Nyquist sampling theorem requirements.

2. Spectral Leakage: DFT truncates time-domain signals by multiplying with a window function (equivalent to convolution in frequency domain). This can be mitigated using alternative window functions like Hanning window (hanning() in MATLAB) or Hamming window (hamming()) instead of rectangular windows to reduce sidelobe effects.

3. Picket Fence Effect: DFT only provides spectral values at discrete sampling points, losing information between points. This can be addressed through zero-padding techniques (using fft(x,N) with N>length(x) in MATLAB) to interpolate spectral components.

These three phenomena represent fundamental considerations in DFT-based spectral analysis.